Coreboot by itself is just a hardware initialization code that basically tells your computer what to do when it turns on (i.e. get the processor running, turn on the RAM chips and get the capacity, then see what can be used for outputting display or serial console).

This is all executed before the user sees anything on the screen, at which point the handover to the payload firmware (i.e. the stuff you'd know as 'the BIOS/UEFI screen') is complete.

The coreboot project do also work with getting the BIOS/UEFI stuff running thru their initialization process as their payload, but the code for these payloads are completely separate projects.

The psp runs at an even lower tier than this so no.